Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 20, 2016

Isoperimetric Regions in Rn with Density rp

  • Wyatt Boyer , Bryan Brown , Gregory R. Chambers , Alyssa Loving and Sarah Tammen

Abstract

We show that the unique isoperimetric regions in Rn with density rp for n ≥ 3 and p > 0 are balls with boundary through the origin.

References

[1] Gregory R. Chambers, Isoperimetric regions in log-convex densities, J. Eur. Math. Soc., to appear. Search in Google Scholar

[2] Jonathan Dahlberg, Alexander Dubbs, Edward Newkirk, Hung Tran, Isoperimetric regions in the plane with density rp, New York J. Math. 16 (2010), 31-51, http://nyjm.albany.edu/j/2010/16-4v.pdf. Search in Google Scholar

[3] Alexander Díaz, Nate Harman, Sean Howe, David Thompson, Isoperimetric problems in sectors with density, Adv. Geom. 12 (2012), 589-619. Search in Google Scholar

[4] Max Engelstein, AnthonyMarcuccio, QuinnMaurmann, Taryn Pritchard, Isoperimetric problems on the sphere and on surfaces with density, New York J. Math. 15 (2009) 97-123, http://nyjm.albany.edu/j/2009/15-5.pdf. Search in Google Scholar

[5] Frank Morgan, Regularity of isoperimetric hypersurfaces in Riemannian manifolds. (English summary) Trans. Amer. Math. Soc. 355 (2003), no. 12, 5041-5052 Search in Google Scholar

[6] Frank Morgan, Manifolds with density, Notices Amer. Math. Soc. 52 (2005), 853-858, http://www.ams.org/notices/200508/ fea-morgan.pdf. Search in Google Scholar

[7] Frank Morgan, Geometric Measure Theory, Academic Press, 4th ed., 2009, Chapters 18 and 15. Search in Google Scholar

[8] Frank Morgan, Aldo Pratelli, Existence of isoperimetric regions inRn with density, Ann. Global Anal. Geom. 43 (2013), 331-365 10.1007/s10455-012-9348-7Search in Google Scholar

[9] Cesar Rosales, Antonio Cañete, Vincent Bayle, Frank Morgan, On the isoperimetric problem in Euclidean space with density. Calc. Var. PDE 31 (2008), 27-46. Search in Google Scholar

Received: 2015-7-21
Accepted: 2016-8-7
Published Online: 2016-9-20

© 2016 W. Boyer et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 1.5.2024 from https://www.degruyter.com/document/doi/10.1515/agms-2016-0009/html
Scroll to top button